Drainage of Agricultural Lands - Practices of Irrigation and On-farm Water Management - page 343

9.3.3.1 Resultant Horizontal Hydraulic Conductivity

Consider a soil column having n layers, and the depth (m) and horizontal hydraulic
conductivity (m/d) of the layers are d 1 , d 2 , d 3 , K n ,

respectively (Fig. 9.9 ) . Assume that the hydraulic gradient in the horizontal direction
is grad

... d n and K 1 , K 2 , K 3 , ...

ϕ .

Fig. 9.9 Schematic of
horizontal hydraulic
conductivity

1 q 1 d 1

K 1

2 q 2

d 2

K 2

3 q 3

d 3

K 3

n q n

d n

K n

The total depth of the layers, D = d 1 + d 2 + d 3 + ... d n

Flow through unit width of layer d 1 under grad ϕ hydraulic gradient, q 1 = A 1 V 1

= (1 × d 1 ) × ( K 1 grad ϕ ) = K 1 d 1 grad ϕ

Similarly,

Flow through “ d 2 ”, q 2 =

ϕ

K 2 d 2 grad

Flow through “ d 3 ”, q 3 = ϕ

K 3 d 3 grad

Flow through “ d n ”, q n = ϕ

K n d n grad

Total flow through the layers,

i = 1

n

Q = q i = ( K 1 d 1 + K 2 d 2 + K 3 d 3 +···+ K n d n )grad ϕ

or,

K i d i grad

Q = ϕ (9.6)

Now, we assume that the equivalent horizontal hydraulic conductivity of the whole
column (layers) is K H (m/d). Then,

d i ×

Q = D × K H grad ϕ = K H grad ϕ (9.7)

where D is the depth of soil column.
Equating the Eqs. ( 9.6 ) and ( 9.7 ) , we get